4 research outputs found

    The number of clones determined by disjunctions of unary relations

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    We consider finitary relations (also known as crosses) that are definable via finite disjunctions of unary relations, i.e. subsets, taken from a fixed finite parameter set Γ\Gamma. We prove that whenever Γ\Gamma contains at least one non-empty relation distinct from the full carrier set, there is a countably infinite number of polymorphism clones determined by relations that are disjunctively definable from Γ\Gamma. Finally, we extend our result to finitely related polymorphism clones and countably infinite sets Γ\Gamma.Comment: manuscript to be published in Theory of Computing System

    Clausal Relations and C-clones

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    We introduce a special set of relations on a finite set, called clausal relations. A restricted version of the Galois connection between polymorphisms and invariants, called Pol-CInv, is studied, where the invariant relations are clausal relations. Clones arising from this Galois connection, so-called C-clones, are investigated. Finally, we show that clausal relations meet a sufficient condition that is known to ensure polynomial time solvability of the corresponding CSP

    Complexity of clausal constraints over chains

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    We investigate the complexity of the satisfiability problem of constraints over finite totally ordered domains. In our context, a clausal constraint is a disjunction of inequalities of the form x≥d and x≤d. We classify the complexity of constraints based on clausal patterns. A pattern abstracts away from variables and contains only information about the domain elements and the type of inequalities occurring in a constraint. Every finite set of patterns gives rise to a (clausal) constraint satisfaction problem in which all constraints in instances must have an allowed pattern. We prove that every such problem is either polynomially decidable or NP-complete, and give a polynomial-time algorithm for recognizing the tractable cases. Some of these tractable cases are new and have not been previously identified in the literature
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